This blog addresses the fatal flaw at the core of capitalism as a system of human psycho-socio-political-economic collective self-reproduction, a flaw which ultimately renders it a self-DIS-organizing, self-destroying system -- as is becoming increasingly evident. It also details the successor system to capitalism, the new system that represents the higher, positive way forward for humanity: Political-ECONOMIC DEMOCRACY, or EQUITISM.

Sunday, December 29, 2013

A Fundamental Inquiry into the Nature of Human Social
Productive Force, and of Its Marxian Conception. Analysis--

A Fundamental Exploration of the Conceptof Social Productive Force.

Dear Readers,

This blog-entry contains my “improvement” of one more text
by theE.A.g. [Equitist Advocacy
group], this one entitled “The Heart and Soul of
Marxian Theory”.

I have provided my
version of their text in the first two parts of this series of blog-entries here, and I am planning to then add two new sections, as the third and fourth blog-entries in this series, setting forth some of the fruits of the
latest research by the Foundation
regarding the critical, immanent ‘extention’
of the central Marxian concept of the "social forces of production", to the concept of the ‘‘‘human-societal[self-]force
ofhuman-societal[self-[re-]]production’’’,
in part via an immanent critique of the ideology-compromised science of Darwinian biology, resulting in
F.E.D.’s theory of ‘Dialectical Meta-Darwinism’ as a positive fruition of that immanent critique.

We have ascertained, in the two preceding Parts, that “The
Heart and Soul of Marxian Theory” is none other than the growth of the
human social forces of production, as one of the two “sides” of the
historical development of the human “social individual”, a topic-heading which
includes, under its heading, the obstacles to that growth, and the
‘overcomings’ of those obstacles, and the effect of the growth of social
productive force upon the other crucial “side” of the development of the human
“social individual”, namely, upon the human “social relations of
production”, and, thereby, also upon the state of human society as a
whole, and upon ‘‘‘the human condition’’’ in its totality.

¿But what, indeed, must the phrase “social productive force(s)”
mean, precisely, in Marxian theory, for it to rightly occupy so central a place
in that theory?

Within the ‘Human Phenome’, the pre-existing concept/meme of
“force” underwent a vast further development through the circa 1666-1687
work of Isaac Newton, especially as a result of the conceptual ‘[re-]foundation’
of modern science that he produced in his monumental treatise, the «Principia»
[translated full title -- Mathematical
Principles of Natural Philosophy].

¿To what extent, if any, is the Newtonian meme of “force”
determinative with respect to the Marxian concept of “social productive force”?

Well, in Newton’s physics, positive force is the cause of motion,
but not just a cause of “uniform motion” -- of mere,
constant, velocity -- but of accelerated motion [or of decelerated
motion, in the cases of, and for the causes of, “negativeforce”].

That is, “stead[il]y” force[d] motion means, in the primary case, that of “positive
force”, an observed gain or growth in the velocity of the
body of mass upon which the force is operating with every passing unit of
time.

Note, here, that, explicitly, Newtonian force is about bodies
of mass, moving, with changing
velocity, in physical space, in response to forces
that arise externally to those bodies, and that impinge
upon them fromoutside of them:external forces.

These terms of reference are largely not adequate to determine the Marxian
concept of social productive force.

That concept is not concerned, directly, with physical,
inertial mass, or with the movement of bodies of mass in physical space, or
with the velocity of that kind of movement, ‘acceleratory’ or otherwise.

¿But are these two memes -- the Newtonian meme of “physicalforce”, and the Marxian meme of “social productive force”
-- still related as two ‘idea-«species»’ of the same, single
‘idea-«genos»’?

Well, the Marxian concept of social productive force shares, with the Newtonian
concept, the attribute of “growing velocity”.

However, in the Marxian ‘idea-«species»’ of
“force”, it is the “velocity ofproduction”, not
the “velocity of a mass-body along a physical-space
trajectory”per se, that is determinative.

That is, the Marxian concept of “productive force” does involve incrementsto the “velocity ofproduction” of goods --
of goods that may become, later on in an account of (the) social productive
force(s), commodities, and later still, commodity-capitals
-- chronologically later in history for a diachronic-dialectical,
or historical-dialectical, account; systematically later
in the order of presentation for a synchronic-dialectical,
or systematic-dialectical, account.

I.e., Marxian “society-productive force” does involve the rate of
production of such goods, such “use-values”.

This rate might be measured as the number
of units of a particular good that is being
finished and "put out", or "out-put", per unit of time --
say per the hour unit of time-measurement.

Or, this rate might be measured as the number
of units of the physical mass of a
particular good that is being finished/output, e.g., per hour unit.

Or, this rate might be measured as the number
of units of money of the unit sales
price of a particular good that is being output per hour unit.

None of these measures of ‘“production-rate”’, or
of ‘production-velocity’, are the same as the classical
measure of “physical velocity” -- the change in the physical-space location of
the body of mass in question, in units of distance, e.g., of miles, per unit of
time, say, again, per hour unit.

Nonetheless, these various ‘‘‘metrical’’’ or ‘measuremental’
definitions of various ‘‘force’’ concepts can all be grasped as qualitatively
different ‘idea-«species»’ of a single ‘idea-«genos»’
concept of ‘“velocity-in-general”’, in an ‘ideo-
systematics’, ‘ideo-classificatory’, systematic/synchronic ‘dialectic of
force’, by which we mean, in a ‘‘‘trans-Platonian’’’, ‘‘‘modernized’’’ version
of Plato’s originating form of explicit dialectics, his «arithmoi
eidetikoi», or “assemblages of idea-units”, categorial-taxonomic dialectics.

The “velocity of production”, or “rate
of production” ‘ideo-«species» of the ‘‘‘velocity-in-general’’’
category is related to classical political-economic concepts of “productivity”,
and of “the productivity of labor”.

As an “accelerator” of the rate of
production, the “social productive force” must be measured
as [incremental] increases in the rate
of production, or in the ‘velocity of production’ -- as increases
in productivity-in-general.

Given the centrality of the wage-labor ‘‘‘factor’’’ of
production in creating ‘capital-productivity’, i.e., capital-profitability,
per Marx’s analysis, by way of surplus-labor, and by way of the surplus-value
of that surplus-labor, social productive force must be measured, from the Marxian,
analytical viewpoint, and, to a degree, from viewpoint of the personifications
of capital, via sustained increases in labor value-productivity,
measured specifically as the number of monetary units of
the sales-price of a given capitalist’s latest batch of goods-commodities
produced, divided by the number of monetary units of a
given capitalist’s unit-purchase-price of labor-power -- wages, or salaries --
used up / consumed in the process of that production.

In terms of the Marxian, dialectical analysis of the actual
‘‘‘productions-process of capitals’’’, this metric can be expressed,
algebraically, as (c + v + s)/v, i.e., as units of exchange-value of the
product produced, divided by units of exchange-value of labor consumed in that
production, with c representing the “constant capital”
[raw materials, machinery wear-and-tear, etc.], “dead
labor”-consumption-costs of production of that goods-commodities output, with v
representing the “variable capital” [wages] “living
labor”-consumption-cost of production of that goods-commodities output, and
with s representing “surplus-value” of the “surplus-labor”
embodied in that goods-commodities output, i.e., the potential gross
profit on that output [setting aside the effects of the process of the
formation of the general rate of profit, on that potential].

In terms of the Marxian analysis of what really matters to
the personifications of capital -- the ‘profit-productivity’
of their capital, or its ‘return on costs invested’ -- this metric becomes the ‘net
gain time-offset self-ratio, or net gain
self-rate, of output in relatio(n) to input’,
where gross output is measured as (c + v + s), and net
output self-rate as, i.e., ‘net
output minus [earlier] input, then also divided by that same [earlier]
input’, in the form ofs’/(c + v),
which has the form of a net Output over Input net
gain ratio, (O - I)/I, and wherein --

s’ = (c + v + s) - c - v - r - i - t - ...

-- i.e., wherein s’ represents the net
surplus-value, the output, net of input [costs of
production], and also net of other deductions, that the
given capitalist must pay to others, e.g., also after the deduction of rent
expenses [part of the revenue supporting the [sub-]class(es) of land
owners], interest expenses [part of the revenue supporting
the [sub-]class(es) of financial capitalists], tax expenses [part
of the revenue supporting the [sub-]class(es) of state bureaucrats],
etc., etc.

In practice, in accord with the kind of consciousness that
is "lawfully" native to the class of the personifications of the
capital-relatio[n], such personifications measure ‘the profit-productivity
of their capital’ as r’/f, where r’ stands for the periodic [say,
annual, or quarterly] net profit return from
sale of the periodic produce / output of their production operation.

Therein, in that ‘‘‘return-on-investment’’’ rate, or
ratio, the variable f stands for that part of Marx’s
dialectical-analytical category of “constant capital” that was not
consumed in the production of the output whose sale generated that net return[ed-value]
numerator.

That is, f stands for the “undepreciated”
portion of the given capitalist’s “capital plant and equipment” value, called
‘“fixed capital value’’’, or '"fixed assets
value"'.

Such “fixed” capital-value is “fixed”
in that it has notyet been “consumed”, and
thereby “converted”, into the product/output which was “circulated” for sale,
and, in fact, actually sold -- or was “realized” -- to generate that return.

The algebraic variable f thus stands for the value of
“capital plant and equipment” that remained fixed in that
accounting period, as opposed toc, the value of the raw
materials, etc. that went entirely into embodiment in the product-output, and
also of the wear-and-tear depreciation / "productive consumption" of
a portion of that, formerlyfixed, portion of the
“capital plant and equipment” value, that also went into “circulating capital”,
along with the “raw materials” value, but in the form of “wear-and-tear”
depreciation expense, reflecting, and compensating the capitalist for, the
“productive consumption” of that capitalist’s “capital plant and equipment”,
the consumption-of-itself-by-its-production-use.

The personifications of capital, in their accounts of
profitability, and in their accounting systems, tend to see their fixed-capital
plant and equipment as the sole source and cause of their
profits-return, and to treat raw materials costs and wages costs
as mere expenses, much like they treat rent expense, interest expense,
tax expense, etc.

All of these metrics might be aptly described as
measurements of ‘theexchange-valueproductivity
of capital-value’, or of ‘the monetary-value productivity
of capital’, or of ‘the potential-new capital-value productivityof capital-value’, or, more simply, as the ‘value productivity
of capital’. [see Marx, «Grundrisse», [Nicolaus translation, p. 630n.]:“*The productivityofcapitalascapital is nottheproductiveforcewhich increases use-values;
but rather its capacity to
create value; the degree to which it produces value.” [emphases addedby M.M.],
thus well-measured by the Marxian ratio --

(O - I)/I = s’/(c + v)].

However, the acceleration of productivity could also be measured as sustained
increases in the number of units, or in the number of the physical mass units,
of a particular good, of its use-value, produced, say, per hour, by the entire
“production entity”, or “human social organization”, that is producing that
use-value: ‘new use-valueproductivity of prior
use-value’, completely side-stepping any reference to monetary[,
exchange]-value units-of-measure.

Indeed, there are many sub-«species» of
metrics for the single «species» of positive “social productive
force”, grasped as sustained productivity ratio growth-qua-sustained-rate-of-increase
of the velocity-of-production.

We will consider the relative merits of various of these sub-«species»
in the final Part of this series, Part 4,
in which we plan to derive a comprehensively-adequate ‘quanto-qualitative’
metric for the Marxian concept of social productive force.

Any of these sub-«species»
of concepts/metrics/definitions of “social productive force” may be applied in
various human-social contexts, and at various human-social scales.

¿What context, and what scale, is the
right scale for an adequate definition of the Marxian
concept of “social productive force”?

To decide this question, let us test our tentative, generic
concept of “social productive force” as “that which ‘sustainedly’ increases
productivity” -- at which we have just arrived by our inquiry so far -- to
various such human-social contexts and scales, so
as to find out, by means of these “thought experiments”, which scale(s)
and which such context(s) (is)(are) definitive for the Marxian
concept of “social productive force”.

Let us order this inquiry by starting from the simplest, most
“human-scale”, most sensuously-concrete, most localized context and scale,
and then consider, consecutively, more complex, larger-scale,
more sensuously-remote, less localized contexts and scales
thereafter.

1.Micro-scale.An individual instrument, e.g., an
individual, hand-held tool, wielded by an individual worker, or an individual
machine, in its productive use, by a human worker, or by a group of human
workers, or by a factory-scale “automatic system of machinery” [cf. Marx, «Grundrisse»,
pp. 692-700], etc., may induce a sustained increment to the 'velocity of
production' of a given product / good / commodity[-capital], relative to the
'velocity of production' obtainable from their predecessor
instrumentalities.This case represents
a growth in the “productive force” of that individual instrument.

Likewise, an individual worker, or a team of workers, by
incremental training, producing, in them, incremental production skills, may
induce a sustained increment to the 'velocity of production' of a given product
/ good /- commodity[-capital], relative to the 'velocity of production' obtainable
from another worker, or from another team of workers, less trained, e.g., from
their previous self or selves, before that worker/that team of workers had
'''consumed''' the incremental training in question.This case represents a growth in the “productive
force” of that individual worker, or of that team of workers as a whole.

Moreover, combinations of these two cases --
of both upgraded instrumentalities and upgraded
worker(s’) skill(s) -- of increases in the “technical composition” of labor-power
[cf. Marx] -- often necessarily occurring together, and in a coordinated
fashion -- may also induce a sustained increment to the 'velocity of production'
of a given product / good / commodity[-capital] -- often, synergistically,
an even bigger such sustained increment than can either kind of upgrade alone
-- relative to the 'velocity of production' obtainable prior to or without such
a combination of upgrades.This case represents a growth in the “productive force” of the ‘‘‘complexunity’’’ of individual workers, or of their
‘‘‘work-force’’’ as a whole, and of their instrumentalities, combined.

2.Meso-scale A.Upgrades to the “technology” of an individual
factory or plant as a whole, i.e., upgrades to production capabilities
embodied in its physical plant, or to the skills of its workforce, or to both,
in concert, may -- e.g., in the context of a multi-factory, or multi-plant,
firm -- induce a sustained increment to the “velocity of production output” of
that entire factory or plant.This case
represents a growth in the “productive force” of an entire, geographically
localized “production complex”.

3.Meso-scale B.Upgrades to the “technology”/“technical
composition of labor” of all or many of the individual factories or plants of a
multi-factory, or multi-plant, firm -- may induce a sustained increment to the
'velocity of production output' of that entire firm. This case represents
a growth in the “social productive force” of the contribution, to the ‘‘‘total
social product’’’, of an entire “individual capital” entity.

4.Meso-scale C.Upgrades to the “social productive force” of most
or many of the individual firms of a geographically-contiguous area, e.g., of
an individual urbanism or municipality, possibly due to the local development,
and/or to a local implementation, of a general advance in, or transition of,
production technology, such as the initial advent of steam-powered industrial
production in certain areas of England, or the initial advent of electrical
machinery, may synergistically induce a ‘‘‘super-additive’’’ aggregate of
sustained increments to the 'velocity of production output' of many
local products. This case represents a growth in “social productive
force” via the contribution, to the ‘‘‘total social product’’’, of, e.g., an
entire city or municipality, possibly facilitated by an epochal advance in
“universal labor”, and resulting technologies.

5.Macro-scale A.Upgrades to the “social productive force” of
many of the individual cities of a geographically-contiguous, multi-urban area,
e.g., of a 'sub-state region', or sub-provincial “region”, may synergistically
induce a ‘‘‘super-additive’’’ aggregate of sustained increments to the
“velocity of production output” of many products, throughout this
"region". This case represents a growth in the “social
productive force” of the contribution, to the ‘‘‘total social product’’’, of,
e.g., an entire sub-provincial “region”.Recent examples:“Silicon
valley”; the city-state of Hong Kong and the nearby portion of its
adjacent coastal province [Guangdong] of mainland China.

6.Macro-scale B.Upgrades to the “social productive force” of
most, or even all, of an entire, ‘sub-national’ “province”, or
'partial-state',may synergistically
induce a ‘‘‘super-additive’’’ aggregate of sustained increments to the
'velocity of production output' of the total [provincial] social product of
this entire province. This case represents a growth in the “social
productive force” of the contribution, to the ‘‘‘total social product’’’, of,
e.g., an entire provincial polity. Recent examples:eventually, the United States of America
nation-state’s "State" of California; eventually, the Chinese
nation-state's province of Guangdong as a whole.

7.Macro-scale C.Upgrades to the “social productive force” of
most, or even all, of an entire “nation-state” may synergistically induce a
‘‘‘super-additive’’’ aggregate of sustained increments to the 'velocity of
production output' of the total [national] social product of this entire nation.This case represents a growth in the “social
productive force” of the contribution, to the ‘‘‘world social product’’’, to
the “global social product”, to the “planetary social product”, of human
society as a whole, i.e., of the “human race”, of the entire, global, planetary
«species» of humanity as a totality, from/by a single,
individual nation-state.Recent
examples:China, India, Brazil.

8.Macro-scale D.Upgrades to the “social productive force” of
most, or even all, of an entire, multi-national, geographically-contiguous
sub-continental “Region” may synergistically induce a ‘‘‘super-additive’’’
aggregate of sustained increments to the 'velocity of production output' of the
total [Regional] social product of this entire multi-national, sub-continental
“Region”.This case represents a growth
in the “social productive force” of the contribution, to the ‘‘‘world social
product’’’, to the “global social product”, to the “planetary social product”,
of human society as a whole, i.e., of the “human race”, of the entire, global,
planetary «species» of humanity as a totality, from/by a
single, individual multi-national, sub-continental “Region”.Recent examples:Asia.

9.Macro-scale E.Upgrades to the “social productive force” of
most, or even all, of an entire continent may synergistically induce a
‘‘‘super-additive’’’ aggregate of sustained increments to the 'velocity of
production output' of the total [Continental] social product of such an entire
multi-national zone.This case
represents a growth in the “social productive force” of the contribution, to
the ‘‘‘world social product’’’, to the “global social product”, to the
“planetary social product”, of human society as a whole, i.e., of the “human
race”, of the entire, global, planetary «species» of
humanity as a totality, from/by a single, individual Continent.Recent examples:North America, Australia, Eurasia.

10.Macro-scale F.Upgrades to the “social productive force” of
most, or even of all, of our planet, e.g., based upon the implementation,
globally, of nuclear fusion power generation, and of plasma technologies in
general, may, in the future, synergistically induce a ‘‘‘super-additive’’’
aggregate of sustained increments to the 'velocity of production output' of the
total [planetary] social product of planet Terra.This case represents a growth in the “social
productive force” of the ‘‘‘world social product’’’, of the “global social
product”, of the “planetary social product”, of human society as a whole, i.e.,
of the “human race”, of the entire, global, planetary «species»
of humanity as a totality:GlobalRenaissance.

We have raised our
perspective regarding the Marxian concept of the ‘“growth of the social force(s” of
production”’, from just one of growth in productivity with
respect to particular kinds of use-values, to one that, in its
totality, grasps this concept as that of the sustainedly rising ‘self-productivity’ of humanity; of ‘human socio-mass’;
as that of the rising ‘rate of human-social reproduction’
in its totality, i.e., in the aggregate, and in the ‘‘‘dynamical system’’’, of
all of the contemporaneous human societies on this planet -- as that of the
rising ‘rate of social
reproduction’ of the Terran human species entire.

The human productive forces, we
hold, must be conceived, not as an ordinary, Newtonian “external force”, as if acting upon
human society “from without”, but, on the contrary, as an “internal force” of human society, and also
as a human societal ‘self-force’, a ‘self-reflexiveforce’.

By the latter, we mean
a force
generated by, and from within, and from out of human society itself, but
also a force
“bending back upon” its source; “bending back” upon itself -- acting back upon, or acting within, and thereby changing,
the very human society from out of which it arises, and thereby also changing itself as well.

Accelerated
‘self-growth’ of ‘human socio-mass’ is the cause
of this force,
and is also its effect.

‘Humansocio-mass’ is the input, and is also the output, and is also the ‘‘‘processor’’’ of that self-same ‘humansocio-mass’ whose sustained self-accelerated
‘self-growth’ expresses, manifests, or materializes, that human society’s ‘societal self-reproductive self-force’.

A partly pictographic
rendering of the first three ‘epoch-specific’, ‘‘‘historically specific’’’
forms of this force is presented below --

As a ‘‘‘rateofreproduction’’’,
a ‘reproductive rate’, this metric also qualifies as kind of a ‘‘‘fitness’’’ metric.

However, this metric
does notmeasure Darwinian
“fitness”, or any kind of “fitness”, of human
individuals, conceived as isolated from human society, or conceived in [e.g., “gladiatorial”] isolation.

It measures the collective,holistic ‘‘‘fitness’’’ of a human society as a whole, as a global
‘‘‘dynamical system’’’; of the human “population” as a whole, or of the
planetary human species
as a totality, only within which can individual human lives subsist and develop.

And it does not measure the collectiveDarwinian “fitness” of the human Genome alone.

It also measures the
human species
self-reproductive fitness of ‘the human Phenome’.

The contributions to
human species
reproductive success of ‘the
human Phenome’ versus those of the “human Genome”
can only be disentangled with great difficulty, if at all.

We mean the “memes
pool” of heritable acquired human characteristics, of learnings, of the fruits
of “universal labor” [Marx], that have their core in spoken human language,
and, later, in written human language, but also encompassing the ideas of the
human mind, and of the human heart, including humanity’s entire range of Mythological, Religious , Philosophical, and Scientific ideas, that are
by now at least as crucial as is the human Genome to the sustained ‘‘‘reproductive
success’’’, survival, and prosperity of the human species.

¿If this is what any metric of Marxian “productive force” must
measure, then how
may we measure it so?

The challenge is this:Our ‘productive force’/‘Meta-Darwinian fitness’
metric needs two components -- one quantifying the contribution of ‘the human
Phenome’, the other quantifying the contribution of “the human Genome”.And both of these components need to be
measured with a common unit of measure, i.e., via a common “dimension”.

The solution of this
conundrum, the detailed, step-by-step framing of an ‘historically-generic’, across-epochs
comparable, [qualo-]quantitative metric for ‘human-societal self-productivity’,
for the self-reproduction rate of ‘human socio-mass’ -- for ‘the human societal
self-reproductive self-force’, and, thus, also, for quantifying the ‘Meta-Darwinian fitness’ of the
human species -- is the focus of our next and final segment of this series.

Next --

Part 4 of 4:Step-by-StepConstruction
of an ‘Historically-Generic’,
‘Qualo-Quantitative’ Metric forHuman-Social Productive Force that is Adequate to its Concept.

Saturday, December 28, 2013

Full Title:F.E.D. Vignette #21, 'On the Dialectical Opposition between the 'FirstStandard Arithmetic',N_, and the Seldonian'FirstDialecticalArithmetic', NQ_', has just been Posted to the www.dialectics.org website.

This essay, especially in its final section, contains substantial material relating to the Marxian, immanent critique of capitalist political economy, and to the ongoing extension of that immanent critique to encompass other 'ideology-compromisedsciences' of the capitalist epoch.

Saturday, December 07, 2013

I usually refrain from posting, here, blog-entries that do not EXplicitly address the dynamics, and the 'meta-dynamics', of the global capitalist economic formation.

However, this time, so seminal is the excerpt, below, on dialectics in general, and, hence, IMplicitly also, on the foundations of the dialectical-mathematical modeling of the [psycho]historical dialectic of the capitalist system, that I have decided to make an exception to my general policy in this specific, exceptional case.

I have reproduced, below, an excerpt from the edited transcript
of a recent, computer-assisted Foundation-internal dialogue with our co-founder, Karl H. Seldon [denoted by "KHS" in the excerpt below],
which the F.E.D. Public Liaison Office has
just cleared for public disclosure.

This is another one of Seldon’s highly-concentrated summaries
of his ground-breaking discoveries in his advancement of Marxian dialectics.

Enjoy!

Regards,

Miguel

“... KHS:What I discovered is that, once demystified, the concept of «karma»
of the Ancient Orient, and the [e.g., Platonian] concept of «autokinesis»
[i.e., of “self-movement”] of the Ancient Occident, contain the seeds of the
keys to the possibility of a new, better comprehension, and to a truly present,
up-to-date mathematical modeling, of our «kosmos».

“Nonlinearity” -- such as that exhibited by, and blocking the
"closed-form" solution of, the differential equation formulations of the most advanced
knowledge of the primary “laws” of Nature achieved by Modern humanity to-date -- is ‘karmicity’ and ‘auto-kinesicity’.

That is, this “nonlinearity” is ‘‘‘self-reflexivity’’’
and ‘self-refluxivity’.

Dialectic is ‘self-reflexive’, ‘self-refluxive’
‘self-«aufheben»-icity’, arising out of the ‘self-duality’, or
‘dialectical self-/internal/immanent "contradiction"’, of ‘Nature-al’ ‘‘‘eventities’’’.

This “nonlinearity” [and its inherent prone-ness to
“singularity”]* is the
manifestation of dialectic within a dialectic-unknowing, ‘‘‘dianoic’’’
[cf. Plato], «verstand»-imprisoned [cf. Hegel], modern mathematics.

‘Deeply-connectedly’, logical and set-theoretical “paradox”
[Bertrand Russell’s diagnosis:these paradoxes are due to “reflexiveness”]
is the form in which dialectic has inescapably manifested itself within a dialectics-denying,
ideologically and polemically ‘‘‘dianoic’’’ “mathematical [‘mathematicized’]
logic” and set theory.

The «kosmos» has constituted itself, in the
past, and continues to constitute itself -- right now -- in
the present, and into the future, as and via a process of
‘self-reflexive self-refluxion’,
described, in the simplest form, via the simplest system of the ‘mathematics of
dialectics’ available to us, by the following formula --

-- wherein, by the term ‘“sub-nuclear
[“non-composite”] particles”’, we
mean the ‘cosmo-ontological category’ that includes “non-composite”
bosons, and
fermions, i.e., for the fermions, the [“non-composite”] quarks, and all
leptons [which, given
their “Pauli Exclusion” behavior, and their lack of “strong interaction”
behavior, are not expected to “compose” -- are not expected to form
“composite” “particles” -- and have not been observed as doing so], and
wherein also the other symbolic-elements of the formula above are
defined as follows
--

[For enhanced legibility, see the enlarged version of the above image at the bottom of this blog-entry.]

For descriptively richer, more complex, more concrete
renditions of the dialectic «modus operandi» of ‘Nature as a
Dialectical Totality’, I also discovered a progression of axioms-systems of
ever more powerful ‘mathematics of dialectics’, which I later found could be
organized -- presented in taxonomic, ‘classificatory’, pedagogically-optimal
order -- and represented compactly, by the following formula, a ‘dialectical
meta-equation meta-model’, formulated in the ideographical language of the first system of “mathematics of
dialectics” that I discovered in 1996
--

-- which instantiates the Marxian, dialectical “method of
presentation” -- that Marx wrote about in his «Grundrisse», and used in organizing and writing his world-historical, world-changing«magnum opus» -- so instantiating by way of generating, in systematic, pedagogical order, a
progressive-cumulative presentation of those axioms-systems of mathematics of
increasing mathematical modeling power, a ‘dialectic of the mathematics of
dialectics’, if you will.

This ‘dialectic of the axioms-systems of explicitly
dialectical mathematics’ starts from 3hN_#_, which
connotes the specification of the axioms-system of the Peano “Natural
Numbers” using only the language of “first-order” symbolic logic, a
specification long known, albeit “non-constructively” so, to harbor “non-standard
models” of “Natural Numbers” arithmetic, hence also of its
algebra.

That 3hN_#_axioms-system of mathematics exhibits a ‘dialecticity’,
or ‘«aufheben»-icity’, that is limited to a simplest, most abstract,
“purely”-quantitative, or “purely”-ordinal, ‘pre-vestige’ thereof, as exhibited in the
‘‘‘ultra-simple’’’ Peano “successor function”, s,
itself -- as ins(n)=n+1.

In that definition, the argument, or operand, of the sfunction, or operator, namely n, which can denote any individual “Natural”
number, is, ‘unifiedly’, transformed in three ways.

It is (1) changed / “negated” [given that n+1 ~=n], (2)“elevated”
in “pure”-quantitative magnitude, or in 'ordinal order-value' [in that n+1>n], and also, at the “same time”, (3)“conserved” [in
that n is “contained in” n+1], i.e., in a single word, is ‘«aufheben»-ated’. ...”

“*[In
simplest, most abstract form, we can illustrate differential equation
‘nonlinearity / singularity’, as it arises within the undergirding system of
arithmetic of the so-called “Real”
Numbers, R, as follows --

dx2(t)/dt=x2(t)( x2(t) )=x2(t)2

-- an ‘“open-form =
closed-form”’-formatted solution of which is the following solution-function, given x2(0)=1 --

x2(t)=t0 + t1 + t2 + t3 + t4 + . .
.=

+(1- t)-1=

+1/(1- t)+1=

1/(1- t)

-- so that a
“singularity” arises at time t=1
--

x2(1) =

1/(1- 1)=

1/0

-- the problem being
that the value / “number” (1/0) does not exist within -- and is "meaningless" within -- the system of the so-called “Real” Numbers, R,
so that, here, suddenly, at the instant
named t=1, the solution of even this ‘‘‘simplest’’’ of
nonlinear differential equations leaps beyond the language-limitations of the numbers-system within which
it was formulated, in an apparently "absolute" kind of apparently "infinitely"-sudden, "infinite"-in-magnitude dis-continuity.

What we have here is a rudimentary mathematical model of a 'non-quantitative' '''revolution''', led up to by a "purely"-quantitative "dynamical evolution" of this '''simplest''' of nonlinear "total--differential", or "ordinary"-differential, equations!

We will release
presentations of the non-“infinite”, ‘meta-finite
meta-number’ value -- a value which is not quantitatively different
from, but which is qualitatively different from, i.e., which is
'ideo-ontologically' different from -- any value available within the R universe of number(s), and which, beginning in the
seventh axioms-system of explicitly dialectical mathematics that arises in the
dialectical progression whose formula we gave above, meaningfully resolves, or
‘semantifies’, such singularities.

We plan to do so soon, and in another venue.

We have been, for the most part, holding back this dialectical discovery for many years.

However,
our 'psychohistorical-dialectical' calculations have indicated that the
time for its public release will soon be "right"]. ...”